Health and Heterogeneity Josep Pijoan-Mas , CEMFI Jos e-V ctor R - - PowerPoint PPT Presentation

Health and Heterogeneity

Josep Pijoan-Mas, CEMFI Jos´ e-V ´ ıctor R ´ ıos-Rull, UPenn and CAERP Society for Economic Dynamics, July 2005

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Introduction

• People are different in many ways: Income and Wealth, Educa-

tion and Marital Status, or Health Related Behavior and Survival Rates.

• As economists, we want to know whether people differ in their

decisions through life because different things happen to them or because they are intrinsically different.

• If the latter, in which dimensions people are different?
• We will exploit data on health outcomes and health investment

to find out.

1

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Death rates and economics (education) are related

Male Mortality Rate by Educational Attainment (years): U.S. 2002.

200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 25–34 35–44 45–54 55–64 Age Group Under 12 12 13 or more

2

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Health measures and economics (education) are related ...

• Self rated health is a very good predictor of mortality (Idler and

and Benyamini, 1997), even when controlling for socio-economic variables and medical conditions. Health share of individ. (%) e = d e = h e = c excellent 9.1 55.5 35.4 very good 11.9 58.7 29.4 good 23.6 58.0 18.3 fair 30.0 60.5 9.5 poor 48.2 42.0 9.9

Note: Males aged 54-59, from HRS.

◮ The proportion of highly educated individuals is increasing by

health category

3

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

... assets and income also matter ... Health Assets Income mean med mean med excellent 194.1 103.8 46.7 34.9 very good 197.4 87.5 45.7 30.5 good 127.0 59.0 32.0 24.6 fair 99.4 34.6 25.6 16.2 poor 40.2 21.6 14.6 10.8

Note: Males aged 54-59, from HRS. Thousands of 1992 dollars.

◮ Both wealth and income increase with the health status

4

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

... even if we separate them. First, conditional on educa- tion wealth still matters; Health e = d e = h e = c mean med mean med mean med

• exc. or v.g.

91.1 45.0 156.42 81.4 303.8 148.2 good 45.2 30.8 125.9 64.0 235.6 122.5 fair or poor 39.4 13.2 97.1 41.4 160.6 65.3

Note: Males aged 54-59, from HRS. Thousands of 1992 dollars.

◮ Conditional on education, the average and median wealth are

also increasing by health category.

5

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

second, conditional on wealth educations matters.

Wealth Health share of individ. (%) e = d e = h e = c Poorest quartile

• exc. or v.g.

22.6 63.7 13.7 good 37.9 52.9 9.3 fair or poor 46.8 46.1 7.1 Second quartile

• exc. or v.g.

14.4 62.9 22.8 good 30.1 57.5 12.3 fair or poor 40.3 53.2 6.5 Third quartile

• exc. or v.g.

7.8 61.2 31.0 good 11.3 68.7 20.0 fair or poor 11.5 78.9 9.6 Richest quartile

• exc. or v.g.

5.1 46.5 48.3 good 6.7 53.3 40.0 fair or poor 13.9 61.1 25.0 Note: Males aged 54-59, from HRS.

◮ Conditional on asset category, the proportion of highly edu-

cated individuals is increasing by health category

6

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Health outcomes and economics (education) are related. Various possibilities of why

• 1. Better education ⇒ more income ⇒ you buy better health.
• 2. Schooling develops different tastes and attitudes.
• 3. Schooling allows to produce better health.
• 4. Old age is relatively more enjoyable with more educ/money.
• 5. There is a (are) third variables(s) that influence both school-

ing and health choices.

7

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Some facts:

• The relationship between health and schooling persists once

we control for income and other socio-economic variables (Gross- man, 1973). Therefore, hypo 1, insufficient.

• A gradient of smoking behavior with years of schooling persists

(and is very strong) when smoking is measured at age 17, before the later years of schooling are completed (Farrell and Fuchs, 1982). Therefore, hypo 2 seems also insufficient.

• Kenkel (1991) shows that the relationship between smoking,

drinking and exercise habits and education persists once we con- trol for individuals knowledge of their effects on health. Hence, hypo 3 not enough.

8

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Health and human capital

◮ Hypos 4 and 5 point to the traditional idea of human capital

investment:

• Human capital, measured as either education or health, re-

quires some investment in the sense that one has to sacrifice current utility in order to build it.

• Any variable affecting the trade-off between current and fu-

ture utilities should equally affect education and health.

• Their respective investments maybe complimentary.

◮ We will try to exploit individual level data on health outcomes,

wealth and education levels to learn about how to think about types of people.

9

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Health investment correlates with education: smoking mar m sing m mar f sing f edu=d 0.32 0.46 0.27 0.32 edu=h 0.21 0.36 0.18 0.27 edu=c 0.12 0.22 0.08 0.13

Note: all individuals, from HRS.

• As known, more educated people smoke less.
• But also females and married people.

10

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Health investment correlates with education: cholesterol tests. mar m sing m mar f sing f edu=d 0.58 0.47 0.68 0.65 edu=h 0.71 0.59 0.73 0.69 edu=c 0.79 0.68 0.80 0.73

Note: all individuals, from HRS.

• More educated people are more likely of having had a choles-

terol test in the last two years.

• Also married individuals and females invest more in health
• The same behavior arises with flu vaccination and breast and

prostrate cancer tests.

11

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Some related work

• Belzil and Hansen (1999) claim that differences in β are im-

portant to explain observed years of education, wages and un- employment, and that discount rates are correlated with ability (more able are more patient).

• Using the NLSY, Munasinghe and Sicherman (2000) show that

non-smokers self select into professions with higher wage growth.

12

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

The Model: Exogenous Variables First the types (fixed heterogeneity),

• Taste for health-related behavior z
• Patience β
• Ability to earn η
• Ability to learn θ

Let τ = {z, β, η} denote a subset of types.

◮ Since we will only focus on first and second moments, we can

state [z, β, η, θ] ∼ N (µ, Σ)

13

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

The Model: Exogenous Variables Next the shocks

• Labor earnings shock ǫ with transition Γǫ,ǫ′
• Shock to health ζ that affects (deteriorates) health, it is i.i.d.

14

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

The Model: Preferences and Endogenous States

• Individuals live for a maximum of I periods.
• Within period utility function, uz (c, y) (health investments).
• Health stock h evolves stochastically h′ = φi(ζ, h, y)
• Health improves survival odds, γi(h).

The endogenous state variables are:

• Education e ∈ E ≡ {e1, e2, ...ene} Chosen when young.
• Wealth a ∈ A ≡ [a, ∞) updated every period.
• Health h ∈ H ⊂ R+ updated every period.

15

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

The Model: the optimization problem

• Agent’s problem at i > 0,

V τ,e,i (ǫ, a, h) = max

c,y,a′,h′

• uz(c, y) + β γi (h) Eζ′,ǫ′|ǫ
• V τ,e,i+1
• ǫ′, a′, h′

with c + a′ = R a + w e η ǫ h′ = ψ

• ζ′, h, y
• Notice that the problem is not indexed by θ.
• At i = 0, youth, individuals choose their education level e.

max

e,y,a′

• W τ,θ

a, a′, e, ǫ, y

• + βγ1 (h) Eζ′,ǫ′|ǫ
• V τ,e,1
• ǫ′, a′, ψ
• ζ′, h, y
• with a yet to be determined current return W(.)

16

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

The Consumption Euler Equation The first Euler equation is standard, uz

c (c, y) = R β γi(h) Eζ′,ǫ′|ǫ

• uz

c

• c′, y′
• If consumption and health related behavior are separable, uz

c (c, y) =

uc(c), then age profiles of c only differ due to {h, ǫ, β}.

• If we only look at retirees (possibly 65 or older to avoid self-

selection), we have uc (c) = R β γi(h) Eζ′

• uc
• c′

◮ Then, If h is observable, the age-profiles for c reveal differences

in time preferences, β. We need a data set containing at the same time health status, income and consumption (or wealth instead

• f consumption).

17

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

The Health Euler Equation The FOC condition: −uz

y (y) = β γi(h) Eζ′,ǫ′|ǫ

• ψy
• ζ′, h, y
• V τ,e,i+1

h

• ǫ′, a′, h′

and the envelope condition: V τ,e,i

h

(ǫ, a, h) = β γi

h (h) Eζ′,ǫ′|ǫ

• V τ,e,i+1

ǫ′, a′, h′ + + β γi (h) Eζ′,ǫ′|ǫ

• ψh
• ζ′, h, y
• V τ,e,i+1

h

• ǫ′, a′, h′

18

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

• It is crucial to identify
• 1. the relationship between health investment and health stock,

h′ = ψ

• ζ′, h, y
• 2. the predictive power of health stocks for survival probabilities,

γi (h)

◮ With information on these two elements, differences in ob-

served y within individuals with same assets a, education e, earn- ings categories ǫ and η and patience β will be accounted for differences in z.

19

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

The Educational Choice Finally, the optimality condition at youth that sorts out people in different educational categories will give us information on the ability to learn or utility cost of education θ once we have already inferred values for β, z and η.

• Note that all the fixed heterogeneity elements, z, β, η and θ

may generate corr (e, h) > 0

◮ By using the model, we want to infer the relative importance

• f each source of fixed heterogeneity and their (possible) corre-

lations.

20

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Mapping the Model to Data

• We needed to know (Possibly only one of them age dependent)
• 1. the relationship health and harmful behavior, ψi ζ′, h, y
• 2. the survival probabilities at different health levels γi (h)
• HRS reports several measures of health stock (self-rated health,

diagnosed conditions) and various measures of health behavior (smoking, exercise habits, cholesterol tests, cancer tests, ...).

• Additionally, HRS reports self-assessed probabilities of survival

to age 75 and 85. Hurd and McGarry (1993, 1995) show they correlate very well with risk factors and that they actually predict mortality.

21

Health and Heterogeneity Josep Pijoan-Mas and V ´ ıctor R ´ ıos-Rull

Targets for Identification of Types

• 1. Given an observation of h, consumption growth identifies β.
• 2. Given an observation of the whole state (ǫ, a, h), variation in

health investment among retirees identifies z.

• 3. We can use earnings analysis directly to get η.
• 4. The positive correlation between education and health.
• 5. The Education Distribution given wage levels per generation

(helps with θ). These variables have to be jointly observed.

22